James Lockhart (banker)
James Lockhart | |
|---|---|
| Born | 1763 |
| Died | 1852 |
| Occupation(s) | Banker, author, mathematician |
| Known for | Numerical analysis, root separation problems in equations |
James Lockhart (1763–1852) was an English banker and author specializing in numerical analysis.
Life
Born as one of three offspring to the Scottish banker James Lockhart (1735–1814) and Mary Harriot Gray, Lockhart received his education at Reading School followed by Eton College. His sibling was John Ingram Lockhart.
Lockhart joined his father’s banking enterprise in London, Lockhart, Wallace, & Co., where he became a partner and established the Cattle Insurance Company. He left the banking profession in 1799 and moved to the Windermere region after the passing of his first wife.
He maintained connections with notable individuals such as Walking Stewart and William Combe, notably impacting Combe’s creation of "Dr Syntax." Lockhart also provided mathematical instruction to both his children and students, including Joshua King.
Beginning in 1819, Lockhart spent approximately fifteen years living in the Netherlands, residing in cities such as Leyden and Haarlem. Upon his brother John’s death without descendants in 1835, he returned to England.
Initially settling in Aylesbury, he relocated to the rectory at Cowley by 1837. Following a legal contest concerning his brother’s will, the Cowley property was sold in 1841, leading him to move to Brompton. By 1847, Lockhart was living at Lanhams near Braintree, Essex.
He acquired shooting rights on the Scottish island of Raasay and spent time on the Isle of Skye. Later, he resided in a mansion in Argyllshire before moving to Clitsome House near Washford, Somerset in 1851, where he passed away the next year.
Works
Lockhart introduced challenging problems related to root separation for fifth- and sixth-degree equations, some of which appeared in print in 1841. While residing in Argyllshire, he continued producing writings on equation theory. His problems had an impact on John Radford Young’s research; William Rutherford highlighted Young’s examination of one such equation posed by Lockhart in an 1849 publication.
In 1842, James R. Christie delivered an extensive study of a quintic equation using Budan's theorem for root separation, which Young referenced. The following year, Young remarked that both Budan's method and Lockhart's concepts could be streamlined based on advancements culminating in Sturm's theorem. Young also praised Lockhart’s publications when addressing a root-related issue originally presented by John Pell to Silius Titus. The work of both Lockhart and Young subsequently influenced Rehuel Lobatto.
Lockhart primarily self-published his contributions, including:
- A Method of Approximating Towards the Roots of Cubic Equations Belonging to the Irreducible Case (1813)
- Nieuwe en algemeene leerwijze om biquadraten op te lossen waarbij de systemas van Descartes en Euler tot biquadraten met derzelver tweede termen worden voortgezet (1823)
- Nieuwe oplossing van cubiek-vergelykingen door juiste uitdrukkingen, en ook bij nadering, zonder beproeving of gissing (1825)
- Extension of the celebrated theorem of C. Sturm, whereby the roots of numeral equations may be separated from each other, with copious examples (1839)
- Resolution of Two Equations (1839)
- Resolution of Equations by Means of Inferior and Superior Limits (1842)
- The Nature of the Roots of Numerical Equations (1850)
Family
Lockhart entered into matrimony twice during his lifetime. His first marriage was to Mary Coxe, the daughter of Leonard Coxe from Philadelphia, who was a loyalist displaced by the American Revolution. Together, they had one son and three daughters. In 1805, he wed his second wife, Elizabeth, with whom he fathered six sons and two daughters; Elizabeth passed away in 1843 at the age of 56. Among Lockhart's offspring were:
- James, the eldest son, known both as a barrister and a poet; his own son, James Augustus Lockhart, served as an officer in the 41st Regiment and died at 21 during the Crimean War in 1855.
- John Ingram (1812–1889), recognized as a writer and associate of Nicolaas Beets.
- Miles, who wedded Anna Rebecca Charlotte, daughter of Major Robert Stewart from the 94th Regiment; their son was James Haldane Stewart Lockhart.
- Maria, who became the wife of John Smith of Ellingham Hall, Norfolk in 1828.